Antenna layer selection and soft demapping for MIMO decoder

ABSTRACT

A MIMO decoder is configured to obtain a channel matrix and generate a Hermitian transpose of the channel matrix. A product of the Hermitian transpose of the channel matrix and the channel matrix is generated to provide a first product having multiple diagonal elements. A partial matrix inversion of the diagonal elements of the first product is generated to provide a diagonal vector. From the diagonal vector, an antenna layer is selected from the multiple antenna layers and represents the antenna layer selected for a given processing iteration. The selected antenna layer will preferably correspond to that having the lowest inverse channel gain. A partial matrix inversion of the first product along the row corresponding to the selected antenna layer is generated to provide a row vector. A product of the row vector and the Hermitian transpose of the channel matrix is generated to provide an inverse channel gain vector.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No. 13/564,305, filed on Aug. 1, 2012, entitled “Antenna Selection for MIMO Decoding”, invented by Eddy Hum and Ming Jia, which is a continuation of U.S. patent application Ser. No. 11/948,644, filed on Nov. 30, 2007, entitled “Antenna Selection for MIMO Decoding”, invented by Eddy Hum and Ming Jia, which claims the benefit of priority to U.S. Provisional Application No. 60/868,176, filed on Dec. 1, 2006. All of the above-identified applications are hereby incorporated by reference in their entireties as though fully and completely set forth herein.

This application is related to U.S. patent application Ser. No. 11/948,675, filed on Nov. 30, 2007, entitled “Soft Demapping for MIMO Decoding” (now U.S. Pat. No. 8,077,788, issued on Dec. 13, 2011), which is hereby incorporated by reference in its entirety as though fully and completely set forth herein.

FIELD OF THE INVENTION

The present invention relates to wireless communications, and in particular to enhanced Multiple Input Multiple Output decoding.

BACKGROUND OF THE INVENTION

Wireless communications have become ubiquitous in modern society, and with the ever-increasing demand for bandwidth, there are significant pressures to increase the effective bandwidth in wireless communication systems. One technique for increasing bandwidth in a wireless communication system is to employ spatial diversity, where different data streams are transmitted from multiple transmit antennas to multiple receive antennas of a receiving device. The data streams may be transmitted from different devices that have a single antenna, from a single device that has multiple antennas, or any combination thereof. Systems that use multiple transmit antennas and multiple receive antennas are generally referred to as Multiple Input Multiple Output (MIMO) systems.

Certain MIMO systems are configured to employ spatial multiplexing, where the different data streams are transmitted at the same time using the same communication resource, such as a particular carrier or sub-carrier. Although each data stream is only transmitted from one transmit antenna, all of the data streams are received at each of the multiple receive antennas. The different data streams propagate over different paths and tend to interfere with one another as they are transmitted from the respective transmit antennas to the receive antennas. As such, a different aggregation of all of the transmitted data streams is received at each of the receive antennas.

To recover each of the originally transmitted data streams from the aggregated signals that are received at each of the receive antennas, the receiving device employs a MIMO decoder. The MIMO decoder essentially processes the aggregated signals to extract each of the originally transmitted data streams. This extraction process is computationally intensive and involves significant amounts of matrix manipulation, such as matrix addition, subtraction, division, inversion, and the like. To further complicate matters, these computations are iterative in nature and generally need to be provided on a symbol-by-symbol basis for each of the transmitted data streams.

While wireless systems are expected to provide ever-higher performance to meet consumer demand, equipment providers are under continuous pressure by service providers and consumers to provide the performance enhancements at lower costs. Unfortunately, computational power and the costs are directly related. Since MIMO decoding is one of the most computationally intensive processes in a MIMO receiver, there is a need for a technique to reduce the complexity of the computations for the extraction process provided by the MIMO decoder. There is a further need to reduce the complexity of the computations without negatively impacting the overall performance of the MIMO receiver.

SUMMARY OF THE INVENTION

The present invention relates to efficient and effective antenna selection in a MIMO decoder for use in a MIMO wireless communication system. Signals that are received via multiple antennas are processed by pre-demodulation circuitry to provide received symbols for use by the MIMO decoder. Channel estimation circuitry is configured to provide channel related information for a channel matrix, which is used by the MIMO decoder and includes channel transfer elements corresponding to different channels in the MIMO wireless communication system. Each column of channel transfer elements in the channel matrix corresponds to one antenna layer of multiple available antenna layers. Each antenna layer is associated with a transmitted data stream that was transmitted from a different transmit antenna. The MIMO decoder is configured to obtain the channel matrix and generate a Hermitian transpose of the channel matrix. The product of the Hermitian transpose of the channel matrix and the channel matrix is generated to provide a first product having multiple diagonal elements.

A partial matrix inversion of the diagonal elements of the first product is generated to provide a diagonal vector. From the diagonal vector, an antenna layer is selected from the multiple antenna layers. The selected antenna layer represents the antenna layer selected for a given processing iteration in the MIMO decoder. The selected antenna layer will preferably correspond to the antenna layer having the highest signal to interference and noise ratio or lowest inverse channel gain. Further, a partial matrix inversion of the first product along the row corresponding to the selected antenna layer is generated to provide a row vector. A product of the row vector and the Hermitian transpose of the channel matrix is generated to provide an inverse channel gain vector, which is used by other functions of the MIMO decoder to facilitate recovery of the transmitted data for each of the antenna layers.

The present invention allows different antenna layers to employ different types of modulation at the same time. As indicated, the diagonal vector represents multiple diagonal elements that may relate to the inverse channel gain for the respective antenna layers. The MIMO decoder may be configured to determine a type of modulation for each of the antenna layers and normalize the diagonal elements of the diagonal vector based on the type of modulation used for each of the antenna layers. Normalization of the diagonal elements compensates for the inherent variability of channel gain that is associated with different types of modulation. In this scenario, the antenna layer is selected based on the normalized diagonal vector.

Those skilled in the art will appreciate the scope of the present invention and realize additional aspects thereof after reading the following detailed description of the preferred embodiments in association with the accompanying drawing figures.

BRIEF DESCRIPTION OF THE DRAWING FIGURES

The accompanying drawing figures incorporated in and forming a part of this specification illustrate several aspects of the invention, and together with the description serve to explain the principles of the invention.

FIG. 1 is a block representation of a MIMO communication environment according to one embodiment of the present invention.

FIG. 2 is a block representation of a receiver according to one embodiment of the present invention.

FIG. 3 is a block representation of a MIMO decoder according to one embodiment of the present invention.

FIG. 4 is a logical flow diagram illustrating operation of an antenna layer selection function according to one embodiment of the present invention.

FIG. 5 illustrates a quadrature phase shift keying (QPSK) symbol constellation according to one embodiment of the present invention.

FIG. 6 is a logical flow diagram illustrating operation of a first embodiment of a soft demapping function according to one embodiment of the present invention.

FIG. 7 is a logical flow diagram illustrating operation of a second embodiment of a soft demapping function according to one embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The embodiments set forth below represent the necessary information to enable those skilled in the art to practice the invention and illustrate the best mode of practicing the invention. Upon reading the following description in light of the accompanying drawing figures, those skilled in the art will understand the concepts of the invention and will recognize applications of these concepts not particularly addressed herein. It should be understood that these concepts and applications fall within the scope of the disclosure and the accompanying claims.

Although the concepts of the present invention may be used in various communication systems, these concepts are particularly applicable to the IEEE 802.16 standard, which is commonly referred to as the WiMAX standard. As illustrated in FIG. 1, a MIMO system 10 will employ multiple transmit antennas TA_(n) and multiple receive antennas RA_(m) to facilitate communications, wherein n and m represent the number of transmit antennas and receive antennas, respectively. Generally, the different receive antennas RA_(m) for a MIMO system 10 are coupled to a single receiver RX of a receiving terminal 12. As depicted, each of a number of transmitting terminals 14 may have one transmitter TX_(n) and an associated transmit antenna TA_(n), where multiple transmitting terminals 14 cooperate to provide MIMO communications with a given receiving terminal 12. In other embodiments, a single transmitting terminal 14 may have and use multiple transmit antennas TA_(n) to support MIMO communications with the receiving terminal 12.

The MIMO system 10 employs the multiple transmit antennas TA_(n), to transmit different data streams TD_(n) to the different receive antennas RAm at substantially the same time while using the same wireless resource, such as a carrier or Orthogonal Frequency Division Multiplexed (OFDM) sub-carrier. In operation, a first transmit antenna TA₁ transmits a first data stream TD₁ using a selected wireless resource, a second transmit antenna TA₂ transmits a second data stream TD₂ using the same wireless resource, and so on and so forth. Since the data streams TD_(n) are transmitted using the same wireless resource at substantially the same time, the data streams tend to combine and interfere with each other in various ways as they propagate toward the receive antennas RA_(m). As such, each receive antenna RA_(m) will receive a different receive signal RS_(m), each of which represents a unique composite of all of the data streams TD_(n) that were transmitted from the different transmit antennas TA_(n). The composite signals are presented to the receiver RX for processing, as will be described further below.

The effective communication path between any one transmit antenna TA_(n) and any one receive antenna RA_(m) is often referred to as a channel. Each channel is associated with a transfer function, h, which represents the impact the particular channel has on the transmitted data streams TD_(n). As illustrated, there are two transmit antennas TA₁, TA₂ and two receive antennas RA₁, RA₂, which use four channels. The transfer function, h_(tr), for each channel is represented where t and r identify the corresponding transmit antennas, TA₁, TA₂ and receive antennas RA₁, RA₂, respectively, for the given channel. Thus, the channel between transmit antenna TX₁ and receive antenna RA₂ has a transfer function h₁₂.

As noted, each received signal RS_(m) is a unique composite of all of the transmitted data streams TD_(n), and in particular, each received signal RS_(m) is a unique composite of all of the transmitted data streams TD_(n) in light of the transfer functions h_(tr) for the corresponding channels. The received signals RS_(m) are mathematically represented in general as follows:

$\begin{matrix} \begin{matrix} \begin{matrix} {{{RS}_{1} = {{h_{11}{TD}_{1}} + {h_{21}{TD}_{2}} + {\ldots\mspace{14mu} h_{n\; 1}{TD}_{n}}}};} \\ {{{RS}_{2} = {{h_{12}{TD}_{1}} + {h_{22}{TD}_{2}} + {\ldots\mspace{14mu} h_{n\; 2}{TD}_{n}}}};} \end{matrix} \\ \vdots \end{matrix} \\ {{{RS}_{m} = {{h_{1m}{TD}_{1}} + {h_{2m}{TD}_{1}} + {\ldots\mspace{14mu} h_{n\; m}{TD}_{n}}}},} \end{matrix}$

and in matrix form as a received signal vector {right arrow over (r)}: {right arrow over (r)}=H{right arrow over (t)}, where:

-   -   the transmitted data stream TD_(n) can be represented by a         vector {right arrow over (t)}=[TD₁, TD₂, . . . TD_(n)];     -   the received signals RS_(m) can be represent as a vector {right         arrow over (r)}=[RS₁, RS₂, . . . RS_(n)]; and     -   the overall transfer function of the MIMO system can be         represented in matrix form by:

$H = {\begin{matrix} h_{11} & h_{21} & \ldots & h_{n\; 1} \\ h_{12} & h_{22} & \ldots & h_{n\; 2} \\ \vdots & \vdots & \; & \vdots \\ h_{1m} & h_{2m} & \ldots & h_{nm} \end{matrix}.}$

The goal of the receiver RX is to recover each of the originally transmitted data streams TD_(n) based on the received signals RS_(m), which are received at each of the receive antennas RA_(m). The receiver can determine the channel transfer functions h_(tr) for each pertinent channel using known channel estimating techniques and create an appropriate channel matrix H for the MIMO system. Since the receiver RX has the received signal vector {right arrow over (r)} and the overall channel matrix H, the receiver RX can readily determine the transmitted data vector {right arrow over (t)}, and thus, each of the transmitted data streams. In particular, since {right arrow over (r)}=H{right arrow over (t)},

-   -   solving for transmitted data vector {right arrow over (t)}         provides:     -   t=H⁻¹ {right arrow over (r)}, where the received signal vector r         and the channel matrix H are known and H⁻¹ is the Moore-Penrose         pseudo inverse of channel matrix H.         This process is equivalent to estimating for X unknown variables         with X or more equations using matrix manipulation. Notably,         each element of the calculated transmitted data vector {right         arrow over (t)} corresponds to a symbol in one of the originally         transmitted data streams TD_(n). Thus, a symbol for each of the         originally transmitted data streams TD_(n) is available once the         transmitted data vector t is calculated.

With reference to FIG. 2, a basic architecture for a receiver RX is illustrated along with two receive antennas RA₁, RA₂. Those skilled in the art will recognize that the receiver RX may be associated with any number of receive antennas. The received signals RS₁, RS₂ are received at the receive antennas RA₁, RA₂, respectively, and processed by pre-demodulation circuitry 16 to recover received symbols for each of the received signals RS₁, RS₂ from the carriers or sub-carriers on which the symbols were originally modulated. For any given period, the pre-demodulation circuitry 16 will provide a received symbol for each of the received signals RS₁, RS₂. Each received symbol represents a composite of the multiple symbols that were transmitted from each of the transmit antennas TA₁, TA₂. The received symbols recovered from each of the received signals RS₁, RS₂ are provided to a MIMO decoder 18. Further, the pre-demodulation circuitry 16 also provides information to channel estimation circuitry 20, which determines transfer functions h_(tr) for the corresponding channels between the transmit antennas TA₁, TA₂ and the receive antennas RA₁, RA₂.

Armed with the transfer functions h_(tr) for the corresponding channels, the MIMO decoder 18 can generate the overall channel matrix H and its Moore-Penrose pseudo inverse (H⁻¹). If the received signal vector is made up of the received symbols from the receive signals RS₁, RS₂, the MIMO decoder 18 can determine the transmitted data vector {right arrow over (t)} by multiplying the Moore-Penrose pseudo inverse of channel matrix (H⁻¹) and the received signal vector {right arrow over (r)}, according to the above derived equation: {right arrow over (t)}=H⁻¹{right arrow over (r)}. Since the elements of the received signal vector r are received symbols, the transmitted data vector comprises the originally transmitted symbols {right arrow over (t)}, which were transmitted from each of the transmit antennas TA₁, TA₂.

The recovered symbols are demapped into corresponding bits based on the type of symbol level modulation used at the transmitters TA₁, TA₂. The symbol level modulation may correspond to quadrature phase shift keying (QPSK), any order of quadrature amplitude modulation (QAM) and any constellation based modulation. Importantly, the present invention supports the use of the same or different types of symbol level modulation by the different transmitters TX₁, TX₂ at the same time. For example, transmitter TX₁ may employ QPSK modulation, while transmitter TX₂ employs 16-QAM or 64-QAM modulation. As a further example, transmitter TX₁ may employ 16-QAM demodulation, while transmitter TX₂ employs 64-QAM modulation. Regardless of the symbol level modulation, the MIMO decoder 18 of the present invention is able to efficiently recover the respective symbols and demap the symbols into corresponding bits, as will be described in further detail below. The recovered bits are passed to the post demodulation processor 22 in association with the originating transmitters TX₁, TX₂ for further processing, as is traditional in the art.

An overview of the basic functional blocks of the MIMO decoder 18 is now provided according to one embodiment of the present invention. As illustrated in FIG. 3, the MIMO decoder 18 may include an antenna layer reduction function 24, antenna layer selection function 26, subset selection function 28, maximum likelihood solution function 30, and soft demapping function 32. Certain of these functions of the MIMO decoder 18 operate in relation to a concept referred to as antenna layers. From the above, all of the transmitted data streams TD_(n) are present in each of the received signals RS_(m). A given antenna layer is a logical representation of those portions of each of the received signals RS_(m) that correspond to a single transmitted data stream TD_(n). In other words, an antenna layer is effectively a cross section of each of the received signals. RS_(m) for a given transmitted data stream TD_(n).

The antenna layer reduction function 24 and the antenna layer selection function 26 cooperate with one another in an iterative fashion. On the first iteration, the antenna layer selection function 26 will select an antenna layer, which is associated with the least inverse channel gain based on the overall channel matrix H, from all of the available antenna layers. Notably, the antenna layer associated with the least inverse channel gain directly corresponds to the antenna layer associated with the highest signal to inference and noise ratio (SINR). The antenna layer selection function 26 will also generate an inverse channel gain vector g _(min) for the selected antenna layer. The inverse channel gain vector g _(min) corresponds to the inverse of a vector corresponding to the channel transfer functions h_(tr) for the selected antenna layer. As will be described further below, the subset selection function 28 will use the inverse channel gain vector g _(min) to generate an estimated transmit symbol {tilde over (s)} for the first transmit layer by multiplying the inverse channel gain vector g _(min) with the received signal vector r. The antenna layer reduction function 24 will proceed with a second iteration based on the selected antenna layer.

On the second iteration, the antenna layer reduction function 24 will remove the channel transfer functions h_(tr) associated with the previously selected antenna layer from the overall channel matrix H to generate a reduced channel matrix H. In this example, reducing the overall channel matrix H effectively removes the column of channel transfer functions h_(tr) that correspond to the previously selected antenna layer. From the remaining antenna layers, the antenna layer selection function 26 will then select another antenna layer that is associated with the least inverse channel gain based on the reduced channel matrix H. The antenna layer selection function 26 will also generate an inverse channel gain vector g _(min) for this newly selected antenna layer.

For subsequent iterations, the antenna reduction layer 24 will remove the channel transfer functions h_(tr) for all of the previously selected antenna layers from the overall channel matrix H to generate an even further reduced channel matrix H. From the remaining antenna layers, the antenna layer selection function 26 will then select yet another antenna layer that is associated with the least inverse channel gain based on the reduced channel matrix H. The antenna layer selection function 26 will also generate an inverse channel gain vector g _(min) for this newly selected antenna layer. This iterative process will continue until each antenna layer has been addressed.

The subset selection function 28 also operates in an iterative fashion in conjunction with the antenna layer selection function 26 and the antenna layer reduction function 24. For the first iteration, the subset selection function 28 estimates the transmitted symbol for the selected antenna layer where, as indicated above, the estimated transmit symbol is referenced as {tilde over (s)}. The estimated transmit symbol {tilde over (s)} may be determined by multiplying the inverse channel gain vector g _(min) for the selected layer by the received signal vector r as follows: {tilde over (s)}= g _(min) r. The inverse channel gain vector g _(min) for the selected layer corresponds to the inverse of a column of channel transfer functions h_(tr), which represents a channel transfer function vector h for the selected antenna layer. Multiplying these vectors results in a single value for the estimated transmit symbol {tilde over (s)}. An estimated transmit symbol {tilde over (s)} for a given layer is an initial approximation of a symbol that was originally transmitted from a corresponding one of the transmit antennas TA_(n).

During the first iteration, the subset selection function 28 may access a constellation reference table, which provides all of the possible constellation points for the selected order of modulation. From the possible constellation points, the subset selection function 28 selects the four closest constellation points that are most proximate to the estimated transmit symbols {tilde over (s)}. The four closest constellation points that are selected represent candidate symbols and referenced as:

-   -   ŝ₁ ⁽¹⁾, ŝ₂ ⁽¹⁾, ŝ₃ ⁽¹⁾, and ŝ₄ ⁽¹⁾.         These candidate symbols ŝ₁ ⁽¹⁾, ŝ₂ ⁽¹⁾, ŝ₃ ⁽¹⁾, and ŝ₄ ⁽¹⁾ are         the four reference symbols deemed most likely to correspond to         the symbol originally transmitted in the first selected antenna         layer. Notably, for QPSK modulation, there are only four         possible constellation points. As such, all of the possible         constellation points are candidate symbols.

For the second iteration, the interference contribution of the first selected antenna layer, which was selected during the first iteration, is effectively subtracted from the received signal vector r. Theoretically, the interference contribution of the first selected antenna layer can be estimated by multiplying the channel transfer function vector {right arrow over (h)} (column of channel transfer functions) for the first selected antenna layer and the actually transmitted symbol s as follows: interference contribution={right arrow over (h)}s. Unfortunately, only the estimated transmit symbol {tilde over (s)} and the candidate symbols ŝ, which were selected based on the estimated transmit symbol {tilde over (s)}, are known at this time. Accordingly, the interference contributions for each of the candidate symbols ŝ of the first selected layer are estimated by multiplying the channel transfer function vector {right arrow over (h)} for the first selected antenna layer and a corresponding candidate symbol ŝ as follows: interference contribution= hŝ. As a result, reduced received signal vectors {right arrow over (r)} for the second iteration are calculated for each of the candidate symbols ŝ identified for the first selected antenna layer as follows: r ⁽²⁾ ={right arrow over (r)} ⁽¹⁾ − hŝ, where r ⁽²⁾ is the received signal vector for the second iteration, and r ⁽¹⁾ is the received signal vector for the first iteration. In particular, since there are four candidate symbols, there will be four corresponding reduced received signal vectors {right arrow over (r)}⁽²⁾ for the second iteration as follows: r ₁ ⁽²⁾ = r ⁽¹⁾ − hŝ ₁ ⁽¹⁾; {right arrow over (r)} ₂ ⁽²⁾ = r ⁽¹⁾ − hŝ ₂ ⁽¹⁾; r ₃ ⁽²⁾ = r ⁽¹⁾ −{right arrow over (h)}ŝ ₃ ⁽¹⁾; and r ₄ ⁽²⁾ = r ⁽¹⁾ −{right arrow over (h)}ŝ ₄ ⁽¹⁾.

For the second iteration, the subset selection function 28 estimates four transmitted symbols for the second selected antenna layer using each of the reduced received signal vectors r ⁽²⁾. This is accomplished by multiplying the inverse channel gain vector g _(min) for the second selected layer by the each of the reduced received signal vectors r ⁽²⁾ as follows: {tilde over (s)} ₁ ⁽²⁾ ={right arrow over (g)} _(min) {right arrow over (r)} ₁ ⁽²⁾; {tilde over (s)} ₂ ⁽²⁾ = g _(min) {right arrow over (r)} ₂ ⁽²⁾; {tilde over (s)} ₃ ⁽²⁾ = g _(min) r ₃ ⁽²⁾; and {tilde over (s)} ₄ ⁽²⁾ = g _(min) {right arrow over (r)} ₄ ⁽²⁾; Again, the inverse channel gain vector g _(min) for the selected layer corresponds to the inverse of a column of channel transfer functions h_(tr), which represents a channel transfer function vector h for the second selected antenna layer.

During the second iteration, the subset selection function 28 will again access the constellation reference table, which provides all of the possible constellation points for the selected order of modulation. From the possible constellation points, the subset selection function 28 selects the four closest constellation points that are most proximate to the each of the four estimated transmit symbols {tilde over (s)}₁ ⁽²⁾; {tilde over (s)}₂ ⁽²⁾; {tilde over (s)}₃ ⁽²⁾; and {tilde over (s)}₄ ⁽²⁾. As a result, there will be 16 candidate symbols, which are represented by:

ŝ_(j,1) ⁽²⁾, ŝ_(j,2) ⁽²⁾, ŝ_(j,3) ⁽²⁾, and ŝ_(j,4) ⁽²⁾, where j=1 to 4 and corresponds to one of the estimated transit symbols {tilde over (s)}_(j) ⁽²⁾ for the second iteration and second selected antenna layer.

This iterative process is provided for each of the available antenna layers. Assuming there are only two antenna layers, the subset selection function 28 will generate and provide four candidate symbols (ŝ₁ ⁽¹⁾, ŝ₂ ⁽¹⁾, ŝ₃ ⁽¹⁾, and ŝ₄ ⁽¹⁾) for the first selected antenna layer along with the sixteen candidate symbols (ŝ_(j,1) ⁽²⁾, ŝ_(j,2) ⁽²⁾, ŝ_(j,3) ⁽²⁾, and ŝ_(j,4) ⁽²⁾, where j=1 to 4) for the second selected antenna layer to the maximum likelihood solution function 30.

Given the nature of the layering, each of the candidate symbols from the first selected antenna layer is associated with a unique set of four candidate symbols from the second selected antenna layer for a two-layer scenario. This association produces sixteen possible symbol pairs, where a symbol pair is made up of one candidate symbol from the first selected antenna layer and one symbol candidate from the second selected antenna layer. As a result, the maximum likelihood decoder solution function processes each of the sixteen pairs of candidate symbols and selects the pair that is most likely to correspond to the pair of symbols originally transmitted from the two transmit antennas TA₁, TA₂. In general, the maximum likelihood solution function 30 compares each pair of candidate symbols to the received signal vector {right arrow over (r)} and determines which one of the candidate pairs most closely matches the received signal vector r. The candidate pair that most closely matches the received signal vector r is selected as the pair of symbols transmitted from the respective transmit antennas TA₁, TA₂ and is referred to as the maximum likelihood solution (MLS). The MLS is a vector of symbols corresponding to the candidate pair, or group if three or more antenna layers are present, and is represented by {circumflex over ( s _(MLS). The MLS vector {circumflex over ( s _(MLS) is provided to the soft demapping function 32. Since the antenna layer having the highest SINR may not have been the first antenna layer, the symbols in the MLS vector {circumflex over ( s _(MLS) may be reordered as necessary to place them in an order in which actual antenna layers are referenced. As such, the soft demapping function 32 is able to associate the symbols in the MLS vector {circumflex over ( s _(MLS) with the corresponding antenna layer.

Each symbol in the MLS vector {circumflex over ( s _(MLS) is associated with a number of bits, depending on the type and order of the modulation. For example, each QPSK symbol represents two bits, each 16-QAM symbol represents four bits, and each 64-QAM symbol represents six bits. As noted, the different antenna layers may support different orders or types of modulation at the same time. The soft demapping function 32 receives the MLS vector {circumflex over ( s _(MLS) and processes each bit of each symbol in MLS vector {circumflex over ( s _(MLS). For each bit, the soft demapping function 32 determines the relative likelihood of the bit being either a logic 0 or logic 1. In particular, the soft demapping function 32 calculates a log likelihood ratio (LLR) for each of these bits based on the channel matrix H and MLS vector {circumflex over ( s _(MLS). The LLR for a given bit is the relative measure of the likelihood that the bit is either a logic 0 or logic 1, which may correspond to an actual 0 and 1 or −1 and 1, respectively. The LLRs for the bits provide the output of the MIMO decoder 18 and are used to recover the originally transmitted bits, which are processed as desired by the post demodulation processor 22.

From the above, the various functions in the MIMO decoder 18 must carry out many computationally intensive mathematical operations, including matrix multiplication, inversion, division, and like manipulation. In particular, the antenna layer selection function 26 and the soft demapping function 32 often require significant matrix manipulations. To compound these issues, the iterative processing nature of these functions has a potential to exponentially increase the number of computations for any given iteration. Different embodiments of the present invention significantly reduce the computational intensity associated with carrying out the functions of the antenna layer selection function 26 and the soft demapping function 32. These embodiments may be used alone or in conjunction in the MIMO decoder 18. A detailed description of a computationally efficient antenna layer selection function 26 is followed by a computationally efficient soft demapping function 32, according to different embodiments of the present invention.

With reference to FIG. 4, a functional block diagram is provided for an antenna layer selection function 26, according to one embodiment of the present invention. As noted above, the objective of the antenna layer selection function 26 is to analyze the channel matrix H and select an antenna layer having the minimum inverse channel gain (or highest SINR) and generate an inverse channel gain vector g _(min) the selected layer. This process is provided in an iterative manner, wherein a different antenna layer is selected for each iteration. Further, the channel matrix H is reduced for each successive iteration by removing the channel transfer functions h_(tr) for the previously selected antenna layers, as described above.

With continued reference to FIG. 4, the illustrated operations are provided during a single iteration, which is operating on an overall or reduced channel matrix H. This iterative process is provided for each carrier or sub-carrier. Once the overall or reduced channel matrix H is available, the antenna layer selection function 26 will generate the Hermitian transpose of the channel matrix H to generate a transposed channel matrix H′ (block 100). The channel matrix H is then multiplied by the transposed channel matrix H′ to generate a product matrix [H′H] (block 102). At this point in traditional antenna layer selection operations, a complete matrix inversion is provided for the product matrix [H′H]. Such operation is extremely computationally intensive.

In one embodiment of the present invention, only a partial matrix inversion of the diagonal elements of the product matrix is provided, wherein the diagonal elements of the partially inverted matrix form a vector, which is referred to as a diagonal vector, referenced as d (block 104). The elements of the diagonal vector generally correspond to the inverse channel gain for the respective antenna layers. The diagonal vector d may be modified by one or more normalization factors μ (block 106). These normalization factors are provided from a look-up table (LUT) (block 108), and correspond to the type of modulation being employed by each of the layers represented in the channel matrix H. Notably, different types of modulation, such as QPSK, QAM, 16-QAM, and the like, are associated with different modulation gains. These different gains have a direct impact on the channel transfer functions h_(tr) in the channel matrix H. The resulting impact generally leads to certain types of modulations always having apparently lower or higher inverse channel gains or SINRs relative to other types of modulation. Accordingly, the antenna layer selection function 26 will effectively normalize the impact of the different types of modulation used in the different antenna layers using gain normalization factors μ.

Each antenna layer may be compensated with a different gain normalization factor μ. In particular, different gain normalization factors may be used to multiply the different diagonal elements in the diagonal vector d based on the type of modulation being employed at each antenna layer. Accordingly, if there are three antenna layers represented in the channel matrix H, each antenna layer may employ a different type of modulation and may be compensated with different gain normalization factors μ. Once the elements in the diagonal vector {right arrow over (d)} are multiplied by any appropriate gain normalization factors μ, a normalized diagonal vector μ d is created. The normalized diagonal vector μ{right arrow over (d)} is then processed to identify the smallest diagonal element in the normalized diagonal vector μ d (block 110). Next, the antenna layer selection function 26 will select the antenna layer corresponding to the smallest diagonal element in the diagonal vector μ d as the selected antenna layer for the iteration (block 112). Again, the selected antenna layer is the one antenna layer that is associated with the least inverse channel gain or maximum SINR. At this point, the product matrix [H′H] is processed such that a partial matrix inversion of the product matrix along the row that corresponds to the selected antenna layer is computed (block 114). The computed row, which is a vector, is then multiplied by the Hermitian transposed channel matrix H′ to generate the inverse channel gain vector g _(min) for the selected antenna layer (block 116).

With reference to FIG. 6, a soft demapping process is provided for an n×m MIMO system, according to one embodiment of the present invention. To facilitate the process, the soft demapping function 32 will receive as inputs: the overall channel matrix H, the MLS vector {circumflex over ( s _(MLS), the diagonal vector d (or other like function of SINR or inverse channel gain), and a residual noise vector {tilde over ({right arrow over (n)}_(r). The overall channel matrix H is an input to the MIMO decoder 18 from the channel estimation circuitry 20. The MLS vector {circumflex over ( s _(MLS) is provided from the maximum likelihood solution function 30. The diagonal vector d is effectively the output of the partial matrix inversion provided by block 104 of the antenna layer selection function 26 illustrated in FIG. 4.

The residual noise vector {tilde over ( n _(r) corresponds to removing the influence of the MLS vector {circumflex over ( s _(MLS) from the received signal vector r, and is calculated as follows: {tilde over ({right arrow over (n)} _(r) = r−H {circumflex over ( s _(MLS), where {right arrow over (r)} represents the received signal vector, H represents the overall channel matrix, and {circumflex over ( s _(MLS) represents the maximum likelihood solution vector. The soft demapping function 32 provides an LLR for each bit that is represented by each candidate symbol ŝ_(MLS) in the MLS vector {circumflex over ( s _(MLS). Different levels of modulation will be associated with a different number of bits, and thus corresponding LLRs. In one embodiment of the present invention, the LLR is calculated as follows:

${{LLR}_{i} = {\left\lbrack {x_{i} + {{Re}\left( {y_{i}^{*}n_{s}} \right)}} \right\rbrack\frac{1}{d}}},$ where LLR_(i) represents the LLR for the i^(th) bit for any given candidate symbol ŝ_(MLS) within the MLS vector {circumflex over ( s _(MLS), d is the element within the diagonal vector d (or other like measure of SINR or inverse channel gain), and n_(s) is a decorrelator value, which is defined further below. The values for x_(i) and y_(i) relate to the distance between the candidate symbol ŝ_(MLS) for the bit being processed, and the closest competitor symbol c_(i). As will be described further below, the values for x_(i) and y_(i) are pre-computed and stored in a look-up table, which is accessible by the soft demapping function 32. By pre-computing these distance related values for x_(i) and y_(i), the computational intensity that is normally required by the soft demapping function 32 is significantly reduced.

The decorrelator value n_(s) represents the residual noise in the normalized constellation plane, and may be calculated as follows:

$n_{s} = {\frac{{\overset{\_}{h}}^{\prime}}{{\overset{\_}{h}}^{2}}{\overset{\_}{\overset{\sim}{n}}}_{r}}$ where {tilde over ( n _(r) represents the residual noise vector, h′ represents the Hermitian transpose of the channel transfer function h for the selected antenna layer, and ∥{right arrow over (h)}∥² represents the squared norm value of the channel transfer function {right arrow over (h)} for the selected antenna layer. This technique for calculating the LLR for each bit of each candidate symbol a ŝ_(MLS) of the MLS vector {circumflex over ( s _(MLS) is unique to one embodiment of the present invention, and represents a significantly improved and very efficient technique for calculating the LLRs.

Prior to providing an example of how these equations may be implemented by the soft demapping function 32, an overview of how the LUT is populated with the appropriate values for x and y is provided. With reference to FIG. 5, a constellation for a QPSK constellation is illustrated. The constellation includes four constellation points: A, B, C, and D. Each constellation point corresponds to a potential symbol in the QPSK constellation, and each symbol represents one of two bits, b₀ and b₁. One of the goals of the soft demapping function 32 is to identify the closest competitor symbol for each bit b_(i). For the illustrated QPSK example, the closest competitor symbol for the candidate symbol ŝ_(MLS) is determined for both bit b₁ and b₀. In this example, assume the candidate symbol ŝ_(MLS) corresponds to symbol D in the QPSK constellation. For symbol D, b₁=1 and b₀=0. Initially, the symbols in the constellation that are competing with b₁ are symbols A and B. This is because symbols A and B correspond to bit b₁=0. Symbol C does not compete with bit b₁ of symbol D, because bit b₁ of symbol C is equal to 1. Since bit b₁=0 for both symbol A and symbol. B, these symbols are considered to be competing symbols. Next, the closest competing symbol to symbol D is determined. Based on proximity, symbol A is closest to symbol D, and as such, symbol A is determined to be the closest competing symbol for bit b₁ of symbol D.

The process is then repeated for bit b₀ of symbol D. Since bit b₀=0 for symbol D, symbols B and C are competing symbols, because bit b₀=1 for symbols. B and C. Of symbols B and C, symbol C is closest to symbol D, and as such, symbol C is selected as the closest competing symbol for bit b₀ of symbol D. An x value and a y value are calculated based on these respective competing symbols A and C.

In one embodiment, each bit b_(i) that has a value of either 0 or 1 can be mapped into a value B_(i) that has a value of either +1 or −1. Accordingly, the following mapping scenarios are possible, depending on whether or not the bits are effectively inverted. Implementation of inversion may be based on any forward error correction that is done in the post demodulation processor 22 during subsequent processing. The first mapping scenario is provided as follows: b _(i)=0 to B _(i)=−1 and b _(i)=1 to B _(i)=+1. An alternative mapping equation is provided as follows: b _(i)=0 to B _(i)=+1 and b _(i)=1 to B _(i)=−1.

From the above, values of x_(i) and y_(i) are pre-computed as follows for each possible scenario: x _(i) =B _(i) |ŝ _(MLS) −ĉ _(i)|² y _(i)=2 B_(i)(ŝ _(MLS) −ĉ _(i)) wherein ŝ_(MLS) is the candidate symbol, and c_(i) is the closest competing symbol for the i^(th) bit.

Notably, each type of modulation may require its own table. For example, if a system supports QPSK, 16-QAM, and 64-QAM, a different table may be provided for each of the three types of modulation. For QPSK modulation, each bit of each potential symbol will likely be associated with 2 (x_(i), y_(i)) value sets. Since each bit may take one of two values, each value will be associated with a (x, y) value set. In the previous example, where the candidate symbol ŝ_(MLS) corresponds to symbol D in the QPSK modulation, b₁=1 will provide 1(x, y) value set; however, if b₁=0, a different (x, y) value set would be provided. The same is true for b₀ of symbol D. Further, each of the other symbols A, B, and C are addressed in a similar fashion. During processing, the soft demapping function 32 need only identify the candidate symbol and select an appropriate (x, y) value set for each bit, depending on the value of the bit, from the LUT, instead of having to calculate the respective (x_(i), y_(i)) value sets on the fly.

With continued reference to FIG. 6, a process is provided for generating the LLR for a particular bit in a candidate symbol ŝ_(MLS). Initially, the soft demapping function 32 will access the overall channel matrix H and select the channel transfer function vector {right arrow over (h)} from the overall channel matrix H for the selected antenna layer (block 200). The norm of the channel transfer function vector h is generated and then squared (block 202). The result is then inverted (block 204), and multiplied by the Hermitian transpose of the channel transfer function vector h (blocks 206 and 208). The result of this multiplication is further multiplied by the residual noise vector {tilde over ( n _(r) to generate the decorrelator value n_(s) (block 210).

During this time, the soft demapping function 32 will also select the candidate symbol ŝ_(MLS) from the MLS vector {circumflex over ( s _(MLS) for the selected antenna layer (block 212). The selected candidate symbol ŝ_(MLS) is used by the LUT to generate corresponding (x_(i), y_(i)) value sets for each bit of the candidate symbol ŝ_(MLS) (block 214). The conjugate of y_(i) is multiplied by the decorrelator value n_(s) (block 216), and the real part of the product (block 218) is added to x_(i) (block 220).

Meanwhile, the soft demapping function 32 will select the diagonal element d from the inverse channel gain vector d for the selected antenna layer (block 222). The diagonal element d is inverted (block 224) and multiplied (block 226) by the output of block 220 (x_(i)+Re(y_(i)*n_(s))) to generate the LLR_(i) for the i^(th) bit in the candidate symbol ŝ_(MLS). Notably, the decorrelator value n_(s) and the inverse channel gain element d will not change for each of the bits of the candidate symbol ŝ_(MLS). As such, the LUT will provide the appropriate x_(i) and y_(i) (or y_(i)*) such that an LLR is generated for each bit of the candidate symbol ŝ_(MLS).

Again, the above process is particularly pertinent for n×m MIMO systems where there are n transmit antennas TA_(n) and m receive antennas RA_(m). The process may be further simplified for 2×m MIMO systems where there are two transmit antennas TA_(n) (n=2) and m receive antennas RA_(m). In a 2×m MIMO system, there are only two antenna layers, because there are only two transmit antennas TA_(n). In one embodiment of the invention, the LLR for a 2×m system for each bit of each candidate symbol ŝ_(MLS) is calculated as follows:

${LLR}_{i} = {\frac{\Delta}{{{\overset{\_}{h}}_{1}}^{2}{{\overset{\_}{h}}_{2}}^{2}}\left( {{x_{i}{\overset{\_}{h}}^{2}} + {{Re}\begin{pmatrix} y_{i}^{*} & {\overset{\_}{h}}^{\prime} & {\overset{\_}{\overset{\sim}{n}}}_{r} \end{pmatrix}}} \right)}$ where h ₁ is a first of two channel transfer functions, h ₂ is a second of the two channel transfer functions, and {tilde over ( n _(r) is the residual noise vector. x_(i) and y_(i) are provided by a look-up table as described above. The Δ represents a determinant of [H′H]⁻¹, where H′ is the Hermitian transpose of the overall channel matrix H.

With reference to FIG. 7, an exemplary process for calculating LLR_(i) for the i^(th) bit of a candidate symbol ŝ_(MLS) for an MLS vector {circumflex over ( s _(MLS) is illustrated. The process follows the preceding equation. Initially, the soft demapping function 32 will select the channel transfer function vector h from the overall channel matrix H for the selected antenna layer (block 300). The Hermitian transpose of the channel transfer function h (block 302) is multiplied by the residual noise vector {tilde over ( n _(r) (block 304).

Meanwhile, the soft demapping function 32 will select a candidate symbol ŝ_(MLS) from the MLS vector {circumflex over ( s _(MLS) for the selected antenna layer (block 306). The candidate symbol ŝ_(MLS) is used by the LUT to select the (xi, yi) value sets for each bit of the candidate symbol ŝ_(MLS) in sequence (block 308). The product of the Hermitian transpose of the channel transfer function vector h and the residual noise vector {tilde over ( n _(r) is multiplied by the conjugate of y_(i) (block 310), and the real part of the resultant product is taken for further processing (block 312).

To facilitate the process, the soft demapping function 32 will take as inputs two squared elements, ∥ h ₁∥² and ∥{right arrow over (h)}₂∥², corresponding to the squared norm of the two channel transfer function vectors {right arrow over (h)}₁ and {right arrow over (h)}₂ respectively. The soft demapping function 32 will select ∥ h∥² from these two squared elements for the selected antenna layer (block 314) and then multiplied by x_(i) (block 316). The resulting product (x_(i)∥{right arrow over (h)}∥²) is added to the real part of y_(i)* h′ {tilde over ( n _(r) (block 318).

In parallel, the squared elements for each antenna layer, ∥ h ₁∥² and ∥ h ₂∥², are multiplied (block 320) and the resulting product is inverted (block 322). The inverted result is multiplied by the aforementioned determinant (block 324) to provide the following:

$\frac{\Delta}{{{\overset{\_}{h}}_{1}}^{2}{{\overset{\_}{h}}_{2}}^{2}}$ The outputs of blocks 318 and 324 are multiplied to generate the LLR_(i) for the i^(th) bit of the candidate symbol ŝ_(MLS) (block 326). As noted above, the LUT will sequentially step through the (x_(i), y_(i)) value sets for each of the bits in the candidate symbol ŝ_(MLS) to generate each of the respective LLRs.

The terms “transmitter,” “transmit,” “receiver,” and “receive” are used only with reference to a given direction for communication link. The respective antennas may act as both receive and transmit antennas depending on the relative direction of communications. Accordingly, the concepts of the present invention may be employed in any type of wireless node, such as a fixed or mobile user element, base station, access point, or the like.

In the above description and the following claims, the terms “row” and “column” are relative terms and may be used interchangeably with respect to one another to identify those elements associated with one another in different dimensions. As such, the column of a matrix may refer to the horizontal elements in the matrix, while the row of a matrix may refer to the vertical elements in the matrix, and vice versa.

Those skilled in the art will recognize improvements and modifications to the preferred embodiments of the present invention. All such improvements and modifications are considered within the scope of the concepts disclosed herein and the claims that follow. 

The invention claimed is:
 1. A method for operating a receiver in a multiple-input multiple-output (MIMO) communication system, wherein the receiver includes a plurality of receiver antennas, wherein a transmitter of the MIMO communication system includes a plurality of transmitter antennas, the method comprising: receiving an estimated transmit vector that includes a plurality of candidate symbols, wherein the candidate symbols are estimates of respective transmit symbols simultaneously transmitted from the respective transmitter antennas; for each of the transmitter antennas, performing a set of operations using electronic circuitry, wherein the set of operations includes: for each bit within each candidate symbol in the estimated transmit vector, computing a soft information value for the bit, wherein said computing the soft information value includes: (a) determining a distance measure x_(i) and a displacement vector y_(i) for the bit, wherein the distance measure x_(i) comprises a measure of distance between the candidate symbol and a closest competing symbol for the bit, wherein the displacement vector y_(i) comprises a complex displacement between the candidate symbol and the closest competing symbol; and (b) computing the soft information value for the bit based on the distance measures x_(i), the displacement vector y_(i) and on a measure d of inverse channel gain for the transmitter antenna.
 2. The method of claim 1, wherein the set of operations also includes: computing a residual noise value corresponding to the transmitter antenna based on a residual noise vector and a column of a channel matrix H, wherein the channel matrix H characterizes a channel between the transmitter antennas and the receiver antennas, wherein said column of the channel matrix H corresponds to the transmitter antenna.
 3. The method of claim 2, wherein said computing the residual noise value corresponding to the transmitter antenna includes: computing a Hermitian transpose of the column corresponding to the transmitter antenna, to obtain a transpose vector; computing a square magnitude of the column; multiplying the transpose vector by an inverse of the squared magnitude to obtain a scaled transpose vector; multiplying the scaled transpose vector by the residual noise vector.
 4. The method of claim 2, wherein the residual noise vector is computed by: multiplying the channel matrix by the estimated transmit vector to obtain a resultant vector; and subtracting the resultant vector from a received symbol vector to obtain the residual noise vector, wherein the received symbol vector includes a plurality of received symbols, wherein each of the received symbols is received through a respective one of the receiver antennas.
 5. The method of claim 2, wherein the soft information value for the bit is computed according to the expression {x_(i)+Re(y_(i)*n_(s))}/d, where Re(y_(i)*n_(s)) denotes the real part of y_(i)*n_(s), where n_(s) is the residual noise value.
 6. The method of claim 2, wherein the measure d of inverse channel gain for the transmitter antenna is computed by: computing an inverse of diagonal elements of a product matrix H′H to obtain a diagonal vector, wherein H′ is the Hermitian transpose of H; and selecting an element of the diagonal vector corresponding to the transmitter antenna.
 7. The method of claim 1, wherein said determining a distance measure x_(i) and a displacement vector y_(i) for the bit is performed by accessing a lookup table using the bit and the candidate symbol.
 8. The method of claim 1, further comprising: supplying the soft information to a processor for recovery of underlying information bits.
 9. A receiver for a multiple-input multiple-output (MIMO) communication system, wherein a transmitter of the MIMO communication system includes a plurality of transmitter antennas, the method comprising: a plurality of receiver antennas; and circuitry configured to: receive an estimated transmit vector that includes a plurality of candidate symbols, wherein the candidate symbols are estimates of respective transmit symbols simultaneously transmitted from the respective transmitter antennas; for each of the transmitter antennas, perform a set of operations, wherein the set of operations includes: for each bit within each candidate symbol in the estimated transmit vector, computing a soft information value for the bit, wherein said computing the soft information value includes: determining a distance measure x_(i) and a displacement vector y_(i) for the bit, wherein the distance measure x_(i) comprises a measure of distance between the candidate symbol and a closest competing symbol for the bit, wherein the displacement vector y_(i) comprises a complex displacement between the candidate symbol and the closest competing symbol; and computing the soft information value for the bit based on the distance measures x_(i), the displacement vector y_(i) and on a measure d of inverse channel gain for the transmitter antenna.
 10. The receiver of claim 9, wherein the set of operations also includes: computing a residual noise value corresponding to the transmitter antenna based on a residual noise vector and a column of a channel matrix H, wherein the channel matrix H that characterizes a channel between the transmitter antennas and the receiver antennas, wherein the column of the channel matrix H corresponds to the transmitter antenna.
 11. The receiver of claim 10, wherein said computing the residual noise value corresponding to the transmitter antenna includes: computing a Hermitian transpose of the column corresponding to the transmitter antenna, to obtain a transpose vector; computing a square magnitude of the column; multiplying the transpose vector by an inverse of the squared magnitude to obtain a scaled transpose vector; multiplying the scaled transpose vector by the residual noise vector.
 12. The receiver of claim 10, wherein the circuitry is configured to compute the residual noise vector by: multiplying the channel matrix by the estimated transmit vector to obtain a resultant vector; and subtracting the resultant vector from a received symbol vector to obtain the residual noise vector, wherein the received symbol vector includes a plurality of received symbols, wherein each of the received symbols is received through a respective one of the receiver antennas.
 13. The receiver of claim 10, wherein the circuitry is configured to compute the soft information value for the bit according to the expression {x_(i)+Re(y_(i)*n_(s))}/d, where Re(y_(i)*n_(s)) denotes the real part of y_(i)*n_(s), where n_(s) is the residual noise value.
 14. The receiver of claim 10, wherein the circuitry is configured to compute the measure d of inverse channel gain for the transmitter antenna by: computing an inverse of diagonal elements of a product matrix H′H to obtain a diagonal vector, wherein H′ is the Hermitian transpose of H; and selecting an element of the diagonal vector corresponding to the transmitter antenna.
 15. The receiver of claim 9, wherein the circuitry is configured to determine the distance measure x_(i) and the displacement vector y_(i) for the bit by accessing a lookup table using the bit and the candidate symbol.
 16. The receiver of claim 9, wherein the circuitry is configured to recover underlying information bits based on the data including the soft information values for the bits of the candidate symbols.
 17. The receiver of claim 9, wherein the receiver is incorporated as part of a mobile device.
 18. A non-transitory memory medium for operating a receiver in a multiple-input multiple-output (MIMO) communication system, wherein the receiver includes a plurality of receiver antennas, wherein a transmitter of the MIMO communication system includes a plurality of transmitter antennas, wherein the memory medium stores program instructions, wherein the program instructions, when executed by one or more processors, cause the one or more processors to implement: receiving an estimated transmit vector that includes a plurality of candidate symbols, wherein the candidate symbols are estimates of respective transmit symbols simultaneously transmitted from the respective transmitter antennas; for each of the transmitter antennas, performing a set of operations, wherein the set of operations includes: for each bit within each candidate symbol in the estimated transmit vector, computing a soft information value for the bit, wherein said computing the soft information value includes: (a) determining a distance measure x_(i) and a displacement vector y_(i) for the bit, wherein the distance measure x_(i) comprises a measure of distance between the candidate symbol and a closest competing symbol for the bit, wherein the displacement vector y_(i) comprises a complex displacement between the candidate symbol and the closest competing symbol; and (b) computing the soft information value for the bit based on the distance measures x_(i), the displacement vector y_(i) and on a measure d of inverse channel gain for the transmitter antenna.
 19. The memory medium of claim 18, wherein the set of operations also includes: computing a residual noise value corresponding to the transmitter antenna based on a residual noise vector and a column of a channel matrix H, wherein the channel matrix H that characterizes a channel between the transmitter antennas and the receiver antennas, wherein the column of the channel matrix H corresponds to the transmitter antenna.
 20. The memory medium of claim 18, wherein the program instructions, when executed by the one or more processors, further cause the one or more processors to implement: supplying the soft information to a post demodulation processor for recovery of underlying information bits. 